Electron Temperature Gradient Modes Research Articles

A Multi Water Bag model of drift kinetic electron plasma

A Multi Water Bag model is proposed for describing drift kinetic plasmas in a magnetized cylindrical geometry, relevant for various experimental devices, solar wind modeling... The Multi Water Bag (MWB) model is adapted to the description of a plasma with kinetic electrons as well as an arbitrary number of kinetic ions. This allows to describe the kinetic dynamics of the electrons, making possible the study of electron temperature gradient (ETG) modes, in addition to the effects of non adiabatic electrons on the ion temperature gradient (ITG) modes, that are of prime importance in the magnetized plasmas micro-turbulence [X. Garbet, Y. Idomura, L. Villard, T.H. Watanabe, Nucl. Fusion 50, 043002 (2010); J.A. Krommes, Ann. Rev. Fluid Mech. 44, 175 (2012)]. The MWB model is shown to link kinetic and fluid descriptions, depending on the number of bags considered. Linear stability of the ETG modes is presented and compared to the existing results regarding cylindrical ITG modes [P. Morel, E. Gravier, N. Besse, R. Klein, A. Ghizzo, P. Bertrand, W. Garbet, Ph. Ghendrih, V. Grandgirard, Y. Sarazin, Phys. Plasmas 14, 112109 (2007)].

Regulation of electron temperature gradient turbulence by zonal flows driven by trapped electron modes

Turbulent transport caused by electron temperature gradient (ETG) modes was investigated by means of gyrokinetic simulations. It was found that the ETG turbulence can be regulated by meso-scale zonal flows driven by trapped electron modes (TEMs), which are excited with much smaller growth rates than those of ETG modes. The zonal flows of which radial wavelengths are in between the ion and the electron banana widths are not shielded by trapped ions nor electrons, and hence they are effectively driven by the TEMs. It was also shown that an E × B shearing rate of the TEM-driven zonal flows is larger than or comparable to the growth rates of long-wavelength ETG modes and TEMs, which make a main contribution to the turbulent transport before excitation of the zonal flows.

High frequency geodesic acoustic modes in electron scale turbulence

In this work the finite β-effects of an electron branch of the geodesic acoustic mode (el-GAM) driven by electron temperature gradient (ETG) modes is presented. The work is based on a fluid description of the ETG mode retaining non-adiabatic ions and the dispersion relation for el-GAMs driven non-linearly by ETG modes is derived. The ETG growth rate from the fluid model is compared with the results found from gyrokinetic simulations with good agreement. A new saturation mechanism for ETG turbulence through the interaction with el-GAMs is found, resulting in a significantly enhanced ETG turbulence saturation level compared with the mixing length estimate. It is shown that the el-GAM may be stabilized by an increase in finite β as well as by increasing non-adiabaticity. The decreased GAM growth rates is due to the inclusion of the Maxwell stress.

Turbulent electron transport in edge pedestal by electron temperature gradient turbulence

We present a model for turbulent electron thermal transport at the edge pedestal in high (H)-mode plasmas based on electron temperature gradient (ETG) turbulence. A quasi-linear analysis of electrostatic toroidal ETG modes shows that both turbulent electron thermal diffusivity and hyper-resistivity exhibits the Ohkawa scaling in which the radial correlation length of turbulence becomes the order of electron skin depth. Combination of the Ohkawa scales and the plasma current dependence results in a novel confinement scaling inside the pedestal region. It is also shown that ETG turbulence induces a thermoelectric pinch, which may accelerate the density pedestal formation.

Inward particle transport at high collisionality in the Experimental Advanced Superconducting Tokamak

We have made the first drift wave study of particle transport in the Experimental Advanced Superconducting Tokamak (Wan et al., Nucl. Fusion 49, 104011 (2009)). The results reveal that collisions make the particle flux more inward in the high collisionality regime. This can be traced back to effects that are quadratic in the collision frequency. The particle pinch is due to electron trapping which is not very efficient in the high collisionality regime so the approach to equilibrium is slow. We have included also the electron temperature gradient (ETG) mode to give the right electron temperature gradient, since the Trapped Electron Mode (TE mode) is weak in this regime. However, at the ETG mode number ions are Boltzmann distributed so the ETG mode does not give particle transport.

Dynamics of Nonlinear Coupling between Electron-Temperature-Gradient Mode and Drift-Wave Mode in Linear Magnetized Plasmas

A high-frequency (∼0.4 MHz) fluctuation is excited by an electron temperature gradient (ETG) perpendicular to magnetic field lines, which is consistent with an ETG mode. When the fluctuation amplitude of the ETG mode exceeds a certain threshold, the mode gradually becomes saturated and a low-frequency (∼7 kHz) fluctuation which is originally caused by a drift wave is enhanced, corresponding to the saturation of the ETG mode. In addition, a nonlinear coupling, specifically, the bicoherence between the ETG mode and the drift wave mode, begins to increase when the ETG strength exceeds the threshold, which simultaneously occurs with the saturation of the ETG mode. Thus, it was determined that the ETG mode stimulates the drift wave mode excitement via multiscale nonlinear interaction between the high-frequency (∼MHz) and low-frequency (∼kHz) fluctuations, which ultimately causes ETG mode energy to be transferred to the drift wave mode.

Evolution of the electron temperature gradient mode in plasmas containing vortex and shear flows

Evolution of the electrostatic potential of the electron temperature gradient (ETG) mode in a plasma with shear and vortex flows, as well as impurity ions, is investigated using a local fluid model. The governing equations are obtained through the Bayly nonmodal approach and solved numerically, so that the evolution of the electrostatic potential is obtained directly. It is found that the ETG mode intensity increases with flow shear, and an intensity minimum occurs when the eccentricity of the vortex flow is at a critical value. In general, impurity ions have a stabilizing effect on the flow-shear-induced secondary instability.

Electron-scale turbulence spectra and plasma thermal transport responding to continuous E × B shear ramp-up in a spherical tokamak

Microturbulence is considered to be a major candidate in driving anomalous transport in fusion plasmas, and the equilibrium E × B shear generated by externally driven flow can be a powerful tool to control microturbulence in future fusion devices such as FNSF and ITER. Here we present the first observation of the change in electron-scale turbulence wavenumber spectrum (measured by a high-k scattering system) and thermal transport responding to continuous E × B shear ramp-up in an NSTX centre-stack limited and neutral beam injection-heated L-mode plasma. It is found that while linear stability analysis shows that the maximum electron temperature gradient mode linear growth rate far exceeds the observed E × B shearing rate in the measurement region of the high-k scattering system, the unstable ion temperature gradient (ITG) modes are susceptible to E × B shear stabilization. We observed that as the E × B shearing rate is continuously ramped up in the high-k measurement region, the ratio between the E × B shearing rate and maximum ITG mode growth rate continuously increases (from about 0.2 to 0.7) and the maximum power of the measured electron-scale turbulence wavenumber spectra decreases. Meanwhile, electron and ion thermal transport is also reduced in the outer half of the plasmas as long as magnetohydrodynamic activities are not important and the L-mode plasmas eventually reach H-mode-like confinement. Linear and nonlinear gyrokinetic simulations are presented to address the experimental observations.

Linear and nonlinear dynamics of electron temperature gradient mode in non-Maxwellian plasmas

The effect of non-Maxwellian distributed ions on electron temperature gradient mode is investigated. The linear dispersion relation of ηe−mode is obtained which shows that the behavior of this mode changes in the presence of superthermal ions. The growth rate of ηe−mode driven linear instability is found and is observed to modify due to nonthermal ions. However, it is found that this leaves the electron energy transport coefficient unchanged. In the nonlinear regime, a dipolar vortex solution is derived which indicates that the dynamic behavior of the vortices changes with the inclusion of kappa distributed ions. The importance of present study with respect to space and laboratory plasmas is also pointed out.

The dependence of H-mode energy confinement and transport on collisionality in NSTX

Understanding the dependence of confinement on collisionality in tokamaks is important for the design of next-step devices, which will operate at collisionalities at least one order of magnitude lower than in the present generation. A wide range of collisionality has been obtained in the National Spherical Torus Experiment (NSTX) by employing two different wall conditioning techniques, one with boronization and between-shot helium glow discharge conditioning (HeGDC+B), and one using lithium evaporation (Li EVAP). Previous studies of HeGDC+B plasmas indicated a strong increase of normalized confinement with decreasing collisionality. Discharges with lithium conditioning discussed in the present study generally achieved lower collisionality, extending the accessible range of collisionality by a factor of two. While the confinement dependences on dimensional, engineering variables of the HeGDC+B and Li EVAP datasets differed, collisionality was found to unify the trends, with the lower collisionality lithium conditioned discharges extending the trend of increasing normalized confinement time, BTτE, with decreasing collisionality when other dimensionless variables were held as fixed as possible. This increase of confinement with decreasing collisionality was driven by a large reduction in electron transport in the outer region of the plasma. This result is consistent with gyrokinetic calculations that show microtearing and electron temperature gradient (ETG) modes to be more stable for the lower collisionality discharges. Ion transport, near neoclassical at high collisionality, became more anomalous at lower collisionality, possibly due to the growth of hybrid TEM/KBM modes in the outer regions of the plasma.

Physics basis of Multi-Mode anomalous transport module

The derivation of Multi-Mode anomalous transport module version 8.1 (MMM8.1) is presented. The MMM8.1 module is advanced, relative to MMM7.1, by the inclusion of peeling modes, dependence of turbulence correlation length on flow shear, electromagnetic effects in the toroidal momentum diffusivity, and the option to compute poloidal momentum diffusivity. The MMM8.1 model includes a model for ion temperature gradient, trapped electron, kinetic ballooning, peeling, collisionless and collision dominated magnetohydrodynamics modes as well as model for electron temperature gradient modes, and a model for drift resistive inertial ballooning modes. In the derivation of the MMM8.1 module, effects of collisions, fast ion and impurity dilution, non-circular flux surfaces, finite beta, and Shafranov shift are included. The MMM8.1 is used to compute thermal, particle, toroidal, and poloidal angular momentum transports. The fluid approach which underlies the derivation of MMM8.1 is expected to reliably predict, on an energy transport time scale, the evolution of temperature, density, and momentum profiles in plasma discharges for a wide range of plasma conditions.

Non-linear saturation mechanism of electron temperature gradient modes

The electron temperature gradient (ETG) mode is a very plausible candidate to explain the large electron particle transport and thermal conduction. Production and identification of slab ETG modes and measurement electron transport have been already reported [X. Wei, V. Sokolov, and A. K. Sen, Phys. Plasmas 17, 042108 (2010); V. Sokolov and A. K. Sen, Phys. Rev. Lett. (2011)]. Now, we develop a theoretical model of non-linear saturation mechanism of ETG mode based on the three wave coupling of an unstable high frequency ETG mode with a damped ETG radial harmonic and a damped ion acoustic (IA) mode. Bicoherence analysis of Columbia linear machine (CLM) data show coupling between ETG modes (∼2.4 MHz) and a low frequency mode (∼50 kHz). The large damping drive of the ETG radial harmonic accompanied by the smaller but finite damping of the IA mode presents an energy sink for the unstable ETG mode, thus causing saturation. This model predicts a saturation level of ∼10% and agrees with the observed levels of ETG modes in the CLM.

Collisionless kinetic-fluid simulation of zonal flows in non-circular tokamaks

Fluid simulation of linear zonal flow damping is done with a closure model based on the collisionless gyrokinetics [Sugama et al., Phys. Plasmas 14, 022502 (2007)]. Simulation results of residual zonal flow for low radial wavenumbers are compared with theoretical formulas for circular and non-circular tokamaks. The effects of the elongation and the triangularity are shown to be properly treated in the closure model. Effects of initial parallel flows on zonal flow evolution are also clarified. An appropriate choice of the initial parallel flow gives a much higher residual level than the conventional result with no initial parallel flow. Besides, the zonal flow simulations are done with the E × B nonlinearity as initial sources, which is evaluated from linear gyrokinetic microinstabilities such as ion temperature gradient modes, trapped electron modes, and electron temperature gradient modes, in order to estimate efficiency of zonal flow generation by the source instabilities.

Electron geodesic acoustic modes in electron temperature gradient mode turbulence

In this work, the first demonstration of an electron branch of the geodesic acoustic mode (el-GAM) driven by electron temperature gradient (ETG) modes is presented. The work is based on a fluid description of the ETG mode retaining non-adiabatic ions and the dispersion relation for el-GAMs driven nonlinearly by ETG modes is derived. A new saturation mechanism for ETG turbulence through the interaction with el-GAMs is found, resulting in a significantly enhanced ETG turbulence saturation level compared to the mixing length estimate.

Experimental study of parametric dependence of electron-scale turbulence in a spherical tokamak

Electron-scale turbulence is predicted to drive anomalous electron thermal transport. However, experimental study of its relation with transport is still in its early stage. On the National Spherical Tokamak Experiment (NSTX), electron-scale density fluctuations are studied with a novel tangential microwave scattering system with high radial resolution of ±2 cm. Here, we report a study of parametric dependence of electron-scale turbulence in NSTX H-mode plasmas. The dependence on density gradient is studied through the observation of a large density gradient variation in the core induced by an edge localized mode (ELM) event, where we found the first clear experimental evidence of density gradient stabilization of electron-gyro scale turbulence in a fusion plasma. This observation, coupled with linear gyro-kinetic calculations, leads to the identification of the observed instability as toroidal electron temperature gradient (ETG) modes. It is observed that longer wavelength ETG modes, k⊥ρs≲10 (ρs is the ion gyroradius at electron temperature and k⊥ is the wavenumber perpendicular to local equilibrium magnetic field), are most stabilized by density gradient, and the stabilization is accompanied by about a factor of two decrease in electron thermal diffusivity. Comparisons with nonlinear ETG gyrokinetic simulations show ETG turbulence may be able to explain the experimental electron heat flux observed before the ELM event. The collisionality dependence of electron-scale turbulence is also studied by systematically varying plasma current and toroidal field, so that electron gyroradius (ρe), electron beta (βe), and safety factor (q95) are kept approximately constant. More than a factor of two change in electron collisionality, νe*, was achieved, and we found that the spectral power of electron-scale turbulence appears to increase as νe* is decreased in this collisonality scan. However, both linear and nonlinear simulations show no or weak dependence with the electron-ion collision frequency, νe/i. Instead, other equilibrium parameters (safety factor, electron density gradient, for example) affect ETG linear growth rate and electron thermal transport more than νe/i does. Furthermore, electron heat flux predicted by the simulations is found to have an order-of-magnitude spatial variation in the experimental measurement region and is also found to be much smaller than experimental levels except at one radial location we evaluated. The predicted electron heat flux is shown to be strongly anti-correlated with density gradient, which varies for a factor of three in the measurement region, which is in agreement with the density gradient dependence study reported in this paper.

Validation of electron temperature gradient turbulence in the Columbia Linear Machine

The electron temperature gradient (ETG) mode, which is a universal mechanism for turbulent electron thermal transport in plasmas, is produced and verified in steady-state, collisionless hydrogen plasma of the Columbia Linear Machine. Electron temperature profiles with strong gradients are produced by DC acceleration in a remote biased mesh and subsequent thermalization. Finite amplitude ∼5%, steady-state oscillations at ∼0.3-0.5MHz (in the plasma frame), with azimuthal wave numbers m∼14-16 and parallel wave number k∥∼0.01cm-1 are measured. The massively parallel gyrokinetic toroidal code is used to study these modes. The results show that in the linear phase, the dispersion relation is consistent with kinetic theory. In the nonlinear stage, very strong nonlinear wave coupling gives rise to an inverse cascade of the energy from the fastest growing high-m modes to low-m nonlinear oscillations, which are consistent with the measured azimuthal mode spectrum. The radial structure of the fluctuation also agrees with the experiment. An inward radial shift of the peak of the potential fluctuation occurs during the nonlinear saturation and fluctuation fingers extend radially out to the edge plasma. Three-wave coupling mechanism is involved in the saturation of ETG modes. The simulations show a power law spectrum of the turbulence which suggests that the renormalization theory is appropriate to interpret the turbulent thermal flux.

Measurements of Electron Thermal Transport due to Electron Temperature Gradient Modes in a Basic Experiment

Production and identification of electron temperature gradient modes have already been reported [X. Wei, V. Sokolov, and A. K. Sen, Phys. Plasmas 17, 042108 (2010)]. Now a measurement of electron thermal conductivity via a unique high frequency triple probe yielded a value of χ(⊥e) ranging between 2 and 10 m(2)/s, which is of the order of a several gyrobohm diffusion coefficient. This experimental result appears to agree with a value of nonlocal thermal conductivity obtained from a rough theoretical estimation and not inconsistent with gyrokinetic simulation results for tokamaks. The first experimental scaling of the thermal conductivity versus the amplitude of the electron temperature gradient fluctuation is also obtained. It is approximately linear, indicating a strong turbulence signature.

Theory of coupled whistler-electron temperature gradient mode in high beta plasma: Application to linear plasma device

This paper presents a theory of coupled whistler (W) and electron temperature gradient (ETG) mode using two-fluid model in high beta plasma. Non-adiabatic ion response, parallel magnetic field perturbation (δBz), perpendicular magnetic flutter (δB⊥), and electron collisions are included in the treatment of theory. A linear dispersion relation for whistler-electron temperature gradient (W-ETG) mode is derived. The numerical results obtained from this relation are compared with the experimental results observed in large volume plasma device (LVPD) [Awasthi et al., Phys. Plasma 17, 42109 (2010)]. The theory predicts that the instability grows only where the temperature gradient is finite and the density gradient flat. For the parameters of the experiment, theoretically estimated frequency and wave number of W-ETG mode match with the values corresponding to the peak in the power spectrum observed in LVPD. By using simple mixing length argument, estimated level of fluctuations of W-ETG mode is in the range of fluctuation level observed in LVPD.

Multi-field/multi-scale turbulence response to electron cyclotron heating of DIII-D ohmic plasmas

The multi-field/multi-scale core (ρ ∼ 0.5–0.8) turbulence response to electron cyclotron heating (ECH) of DIII-D Ohmic plasmas is reported for the first time. Long wavelength (low-k) electron temperature (T̃e/Te) and high-k density turbulence levels (ñe/ne) are observed to strongly increase during ECH. In contrast, low-k and intermediate-k ñe/ne showed little change, whereas the cross-phase between local low-k electron temperature and density fluctuations (αneTe) was significantly modified. The increase in the electron thermal diffusivity determined from power balance is consistent with the increased turbulent transport correlated with the measured increases in low-k T̃e/Te and high-k ñe/ne. Linear stability analysis using the trapped gyro-Landau fluid (TGLF) model indicates an enhanced growth rate for electron modes [e.g., trapped electron mode (TEM)] at low-k consistent with the observed modifications in T̃e/Te and αneTe. TGLF also predicts an increase in high-k electron mode growth rates for normalized wavenumbers kθρs > 7, where electron temperature gradient (ETG) modes exist, which is consistent with the observed increase in high-kñe/ne turbulence

Suppression of Electron Temperature Gradient Turbulence via Negative Magnetic Shear in NSTX

Negative magnetic shear is found to suppress electron turbulence and improve electron thermal transport for plasmas in the National Spherical Torus Experiment (NSTX). Sufficiently negative magnetic shear results in a transition out of a stiff profile regime. Density fluctuation measurements from high-k microwave scattering are verified to be the electron temperature gradient (ETG) mode by matching measured rest frequency and linear growth rate to gyrokinetic calculations. Fluctuation suppression under negligible E×B shear conditions confirm that negative magnetic shear alone is sufficient for ETG suppression. Measured electron temperature gradients can significantly exceed ETG critical gradients with ETG mode activity reduced to intermittent bursts, while electron thermal diffusivity improves to below 0.1electron gyro-Bohms.